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104   NATURAL INHERITANCE.   [caar.

crown of the head, upwards or downwards as the case may be, and not from the ground to the crown of the head. (In the population with which I am now dealing, the level of mediocrity is 684 inches (without shoes).) The law of Regression in respect to Stature may be phrased as follows ; namely, that the Deviation of the Sons from P are, on the average, equal to one-third of the deviation of the Parent from P, and in the same direction. Or more briefly still:-If P + (=I= D) be the Stature of the Parent, the Stature of the offspring will on the average be P + (=i= 3 D).

If this remarkable law of Regression had been based only on those experiments with seeds, in which I first observed it, it might well be distrusted until otherwise confirmed. If it had been corroborated by a comparatively small number of observations on human stature, some hesitation might be expected before its truth could be recognised in opposition to the current belief that the child tends to resemble its parents. But more can be urged than this. It is easily to be shown that we ought to expect Filial Regression, and that it ought to amount to some constant fractional part of the value of the MidParental deviation. All of this will be made clear in a subsequent section, when we shall discuss the cause of the curious statistical constancy in successive generations of a large population. In the meantime, two different reasons may be given for the occurrence of Regression ; the one is connected with our notions of stability of type, and of which no more need now be said ; the other is as follows:-The child inherits partly from his